Problem: The equation of a circle $C$ is $x^2+y^2+4x+2y+4 = 0$. What is its center $(h, k)$ and its radius $r$ ?
To find the equation in standard form, complete the square. $(x^2+4x) + (y^2+2y) = -4$ $(x^2+4x+4) + (y^2+2y+1) = -4 + 4 + 1$ $(x+2)^{2} + (y+1)^{2} = 1 = 1^2$ Thus, $(h, k) = (-2, -1)$ and $r = 1$.